Kidney tranplantation is the treatment of choice for most patients with end stage renal disease. However, immune sensitization to HLA antigens makes it difficult to find immunologically compatible renal allografts for up to 30 percent of the end stage renal disease population. Patients with a high percent of preformed for antibodies must wait considerably longer than the average two years for a suitably matched kidney, and in many cases are unable to be tranplanted at all. To date, there is no proven treatment that can result in the reduction in preformed antibodies. The hypotheses of the study are: Anti-idiotypic antibodies present in IVIG preparations have the ability to reduce anti-HLA antibody activity in vivo and in vitro; IVIG contains antibodies that block alloactivation in the standard MLR and could be beneficial in reducing allosensitization post transplant; IVIG inihibits anti-endothelial cell antibody activity and could have a beneficial effect in the prevention and treatment of vascular rejection episodes mediated by AECA; and IVIG treatment has the capacity to induce the blocking anti-idiotypic antibody synthesis by the recipients B cells and thus engender a long lasting suppression of alloreactive events and possibly enhance allograft survival. The proposed clinical trial is a multicenter study involving 100 patients from seven transplant centers scattered throughout the United States. Patients with end stage renal disease, awaiting renal tranplantation, and with preformed cytotoxic antibody levels of greater than 50 percent will be eligible for participation. Patients will be randomly assigned to receive either albumin placebo or IVIG at study entry and at 1, 2, 3, 12, and 24 months following enrollment. If the patient is transplanted any time during the 30 month trial, they will receive IVIG at the time of tranplantation and at 1, 2, 3, 12, and 24 months post transplantation.